What is the physical foundation of Force Fields?
The "practical" definition of these parameters is here:


  Force Fields in the manual


I don't think there is much documentation about their workings under the hood. 

Anyway, each Force type implements one particular type of force in Newton physics. 

Forces, the $\mathbf{F}$ in the second law of motion $\mathbf{F}=m\cdot\mathbf{a}$, are the entities that cause an acceleration $\mathbf{a}$ on a object of mass $m$. Different kind of forces can be described as a function that depends on several features of the object being acted on, or of the space in which the force acts:

$$\mathbf{F} = \mathbf{F}(\mathbf{r}, \mathbf{u}, m, q; \mathbf{r_0}, \eta, \ldots)$$

($\mathbf{r}, \mathbf{u}$ = position and velocity vectors of the test object, $m, q$ = mass and charge of the test object, $\mathbf{r_0}$ = position of the effector object, $\eta$ = viscosity of the medium, ...).

Each force can or cannot depend on each of these variables, and it may depend on them in different ways.


Wind is an acceleration field with a total translational symmetry, if the falloff is 0 and there is no min/max distance, or a 2D translational symmetry otherwise. It doesn't depend on anything except its own force parameters and, if falloff is enabled, on $\mathbf{r_0}$
Force and Charge are (typically spherically symmetric) central force fields (they are aligned along the $\mathbf{r}-\mathbf{r_0}$ direction), the latter depending on $q$
Harmonic is a Hookean field. Same variables as Force, but a different equation.
Drag is a force depending on the object's velocity $\mathbf{u}$ according to Stoke's or Rayleigh's law


and so on.

Within each type of force, there are options that control the overall strength (Force Strength, a parameter that basically appears the $\mathbf{F}$ functions above as a multiplying factor); allow to tweak the dependence of the strength on the distance from the emitter (Falloff, ...); convert part of the dependence on $\mathbf{r}$ to dependence on $\mathbf{u}$ (Flow); ...